To register calves out of a flush, you will need to get the cow TH/PHA tested and DNA. (Is she a Shorthorn?) If you are going to keep the calves you may not be concerned about TH/PHA, but if you want to market the embryos or the offspring positive TH/PHA might affect their marketability. For what it costs to harvest embryos, you want to be sure of marketability.
If you are going to use a sire that has never been used on her, you might get a natural calf out of that mating to see what you get.....again thinking of marketability. Keep in mind that one calf is still no guarantee, but it is a barometer. In an ideal world name recognition of your cow and the bull should not matter...just the quality of the calves....but name recognition is important in marketing.
The market is getting flooded with embryos and there are a lot of $150-$200 embryos out there. Selling them at that price just doesn't make enough money to fool with the aggravation. Please understand I am in no way implying that your cow does not have good calves, it's just that you will have a lot of competition if you try to sell the embryos.
I have always said that flushing is not for the faint of heart. It is a challenge.
Whatever you decide, I wish you the best.